In transmitting data, the data to be transmitted must generally be modulated onto some kind of transmission signal. Although many options exist, one possible transmission signal for use with data modulation is a chirp signal. A chirp signal is a short duration signal whose frequency increases or decreases with time. If its frequency increases, the chirp signal is called an up-chirp; and if its frequency decreases, the chirp signal is called a down-chirp. The rate at which the frequency changes over time is called the chirp's ramp rate. Chirp signals can also be called sweep signals.
Chirp signals can vary their frequency and numerous ways. However, two common types of chirp signals are linear chirps, in which the frequency of the chirp signal increases in a linear fashion, and exponential chirps in which the frequency of the chirp signal increases in an exponential fashion.
A linear chirp can be described in the frequency domain according to equation (1):f(t)=f0+rt  (1)
where f0 is a starting frequency at a time t=0, and r is the linear ramp rate.
A linear chirp can be described in the time domain according to equation (2):
                                                                        x                ⁡                                  (                  t                  )                                            =                              sin                [                                  2                  ⁢                  π                  ⁢                                                            ∫                      0                      t                                        ⁢                                                                  f                        ⁡                                                  (                                                      t                            ′                                                    )                                                                    ⁢                                                                                          ⁢                                              ⅆ                                                  t                          ′                                                                                                                    ]                                                                                        =                              sin                [                                  2                  ⁢                  π                  ⁢                                                            ∫                      0                      t                                        ⁢                                                                  (                                                                              f                            0                                                    +                                                      rt                            ′                                                                          )                                            ⁢                                              ⅆ                                                  t                          ′                                                                                                                    ]                                                                                        =                              sin                [                                  2                  ⁢                                      π                    (                                                                                            f                          0                                                ⁢                        t                                            +                                                                        rt                          2                                                2                                                              )                                                  ]                                                                        (        2        )            
An exponential chirp can be described in the frequency domain according to equation (4):f(t)=f0rt  (3)
where f0 is a starting frequency at a time t=0, and rt is the exponential ramp rate.
                                                                        x                ⁡                                  (                  t                  )                                            =                              sin                [                                  2                  ⁢                  π                  ⁢                                                            ∫                      0                      t                                        ⁢                                                                  f                        ⁡                                                  (                                                      t                            ′                                                    )                                                                    ⁢                                                                                          ⁢                                              ⅆ                                                  t                          ′                                                                                                                    ]                                                                                        =                              sin                [                                  2                  ⁢                                      π                    ·                                          f                      0                                                        ⁢                                                            ∫                      0                      t                                        ⁢                                                                  (                                                  r                                                      t                            ′                                                                          )                                            ⁢                                              ⅆ                                                  t                          ′                                                                                                                    ]                                                                                        =                              sin                [                                  2                  ⁢                                      π                    ·                                                                  f                        0                                            (                                                                                                    r                            t                                                    -                          1                                                                          ln                          ⁡                                                      (                            r                            )                                                                                              )                                                                      ]                                                                        (        4        )            
In each case, the chirp signal will include both the fundamental frequency described by the above equations, as well as accompanying harmonics.
Chirp signals are used commonly in radar and sonar applications. Therefore, there are many systems in existence for sending, receiving, and otherwise manipulating chirps. As a result, it is very relatively straightforward to design a system in which data is modulated onto a chirp. Furthermore, this makes it possible to reuse both a processor and processing resources for both radar and communication functions. It can also take advantage of the radar to provide synchronization and EQ training for communications.
In addition, chirp signals can be used that have a very low peak-two-average ratio (PAR), which can minimize required supply voltages, allow for the use of smaller and more efficient transistors than higher voltage signals.
However, data throughput is always an issue with any data transmission system. It is generally desirable to pass the greatest amount of data in the shortest time possible. As a result, it would be desirable to provide a chirp-based system in which multiple bits of data could be transmitted at the same time.